Describing the problem - Linear Example

Counting the number of observations of each group.

same_group_count_matrix <- 
  with(same_group_df,
       table(x1c, x2c))

same_group_count_matrix

##            x2c
## x1c         (0,0.2] (0.2,0.4] (0.4,0.6] (0.6,0.8] (0.8,1]
##   (0,0.2]        51         0         0         0       0
##   (0.2,0.4]       0        40         0         0       0
##   (0.4,0.6]       0         0        35         0       0
##   (0.6,0.8]       0         0         0        55       0
##   (0.8,1]         0         0         0         0      34